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15 include "basic_2/reducibility/fpr.ma".
17 (* CONTEXT-FREE PARALLEL CONVERSION ON CLOSURES *****************************)
19 definition fpc: bi_relation lenv term ≝
20 λL1,T1,L2,T2. ⦃L1, T1⦄ ➡ ⦃L2, T2⦄ ∨ ⦃L2, T2⦄ ➡ ⦃L1, T1⦄.
23 "context-free parallel conversion (closure)"
24 'FocalizedPConv L1 T1 L2 T2 = (fpc L1 T1 L2 T2).
26 (* Basic properties *********************************************************)
28 lemma fpc_refl: bi_reflexive … fpc.
31 lemma fpc_sym: bi_symmetric … fpc.
32 #L1 #L2 #T1 #T2 * /2 width=1/
35 (* Basic forward lemmas *****************************************************)
37 lemma fpc_fwd_fpr: ∀L1,L2,T1,T2. ⦃L1, T1⦄ ⬌ ⦃L2, T2⦄ →
38 ∃∃L,T. ⦃L1, T1⦄ ➡ ⦃L, T⦄ & ⦃L2, T2⦄ ➡ ⦃L, T⦄.
39 #L1 #L2 #T1 #T2 * /2 width=4/